The study of particle-fluid flow in narrow, curved slots to enhance comprehension of particle transport mechanisms in complex fractures
Introduction
The particle-fluid flow is vital for a wide range of scientific and industrial processes. Typical examples include sand deposition in rivers and lakes, pipeline slurry flow, fluidized bed, etc. In petroleum engineering, particle driven by fluid within complex fracture systems is fundamental in improving reservoir conductivity for oil and natural gas production. Considerable literature has recently grown around the theme of particle transport and distribution in complex fractures by experiments and numerical simulation methods (Xiong et al., 2020; Chun et al., 2020; Li et al., 2018; Hu et al., 2018a; Zhang et al., 2019; Wu et al., 2019). Studies show that many factors, including fracture shape, influence particle placement (Li et al., 2018; Zhang et al., 2019; Sahai and Moghanloo, 2019; Zeng et al., 2016). Experimental investigation and mine-back evidence demonstrate that the common occurrence is different kinds of irregular fracture morphology, including branched fracture, T-shaped fracture, curved fracture (Warpinski and Teufel, 1987; Fu et al., 2019; Dahi Taleghani and Olson, 2013; Lee et al., 2014). The violent interaction between slurry and complex boundaries can significantly affect particle migration and deposition (Fu et al., 2019; Lee et al., 2014; Wang et al., 2019). The transport mechanisms are more complicated in complex fractures than the vertical planar fracture (Jeffrey, 2013).
Previous experimental works conducted in various scaled planar slots mimicked straight fractures and founded three primary transport mechanisms, such as the bed load, turbulence, and viscous drag. Kern et al. (Kern et al., 1959) carried out the first sand-water mixture flow in a straight planar slot that was 0.56 m long, 0.25 m tall, and 6.35 mm wide. He observed that the sand bed in a narrow slot would develop to a dynamic equilibrium with an equilibrium height after a period of injection. Correspondingly, the equilibrium velocity was reached in the flow gap above the bed. The bed load, including fluidization and settlement, transports the later injected sands to the backside of the bed continuously. Increasing fluid velocity induced particle erosion that lowered the bed height. Based on experimental results, Babcock, et al. (Babcock et al., 1967) and Alderman and Wendorff (1970) proposed correlations to predict the height and velocity at equilibrium. They observed the peculiar entrance effect that turbulence near the slot entrance produced more eddies, which carried particles further into the slot and thus left a depleted zone without particles. Medlin et al. (Medlin et al., 1985) also observed the entrance effect in the straight slot and pointed out the viscous drag was the only transport mechanism under field conditions as the high-viscosity fluid carried particles. Patankar et al. (Patankar et al., 2002) carried out experiments in a long straight slot (length 2.44m × height 0.305m × width 8.0 mm) and derived a power law correlation to predict the gap height between the top of the bed and the top of the slot. The correlation is only valid when clean fluid is pumped. Subsequently, Wang, et al. (Wang et al., 2003) proposed two Bi-power law correlations for predicting the equilibrium height, which was widely used to calibrate numerical simulation models and compare experimental results. In addition, Woodworth and Miskimins (2007) applied the correlations to calculate the bed height in a filed scale fracture. The walls with variable apertures and asperities significantly affect slurry flow and particle distribution (Liu, 2006; Raimbay et al., 2016; Huang et al., 2018). Recently, new fracturing fluids, such as high viscosity guar gum, foam fluid, and supercritical carbon dioxide, were tested in straight slots to study transport mechanisms (Tong et al., 2018; Hou et al., 2019; Sun et al., 2018; Boyer et al., 2014).
To understand the particle travel in complex fracture systems, complex slot experimental apparatuses were set up to mimic irregular fracture geometries. Sands mixed with water were injected to a primary straight slot owned several secondary and tertiary slots (Sahai and Moghanloo, 2019; Wen et al., 2016; Sahai et al., 2014; Manoorkar et al., 2016). Two mechanisms were concluded: 1) gravity effect, proppant falling down from the primary dune; 2) suspension effect, proppant flowing around the intersection corner at a fluid velocity higher than a threshold value. The turbulent flow and eddies were observed at fracture intersections once the fluid velocity increases to a high value, which would affect particle distribution. Li et al. (Li et al., 2017) conducted a large-scaled laboratory test to perform sensitivity analysis for branched fracture. The experimental slot was varied the angle between the primary slot and branched slot from 30° to 90°. The important observation is that the coverage area of the bed in the branched slot would increase with the increase of the angle. Tong and Mohanty (2016) had a similar found in a smaller branched slot. Particle transport and distribution were immensely varied in T-shaped slot and inverted T-shaped slot (Chun et al., 2020). The strong turbulent effect would prevent particle travel into the lower horizontal slot and promote them to flow into the upper horizontal slot.
Overall, above extensive studies indicate that the fracture shape could significantly change the particle distribution, which directly affects the fracture conductivity and well production. However, there has been no detailed investigation of particle distribution in curved fractures except the simple straight fractures and complex fractures. Also the curved fracture is a typical and fundamental fracture shape in the complex fracture system. The purpose of this investigation is to explore the relationship between the particle-fluid flow and the curved slot with two bends. The two bends’ angles are the same, which vary from 45° up to 135° (Three angles used 45°, 90°, 135°). Also, a straight slot is used to compare the experimental results of the curved slots quantitatively. The article is organized as follows: in Section 2, experimental methods and procedures are introduced for describing various particles flowed in three curved slots and one straight slot. In Section 3, the equilibrium height of the bed deposited in the straight slot is validated with the correlation proposed by Wang et al. (Wang et al., 2003). Then, sensitivity analysis is performed on the effect of bending angle, fluid velocity, particle size, particle density, and particle volume fraction. A correlation is developed for predicting the normalized coverage area.
Section snippets
Experimental slots
The acrylic sheets were chosen to set up the curved slot. Because of good toughness, a sheet is easily bent several times. Also, high transparency allows us to observe particle-fluid flow closely. Fig. 1(a) shows the isometric view of the curved slot with two bends with 45° as an example of curved slots. Two bends separate the slot into three parts, named the first straight section, the bending section, and the second straight section. Fig. 1(b) illustrates the straight slot, representing the
Validation
Experiments were first conducted in the straight slot. According to the particle distribution in the slot, the nine bed profiles were digitized by the program of GetData Graph Digitizer, as shown in Fig. 4. The fluid velocity and particle density have strong effects on the particle distribution. With the increase of fluid velocity, particles travel deeper into the slot and accumulate the bed far away from the inlet. When the fluid velocity is 0.21 m/s, the flow pattern is laminar, the ceramic
Discussion
Based on the results of the experimental investigation in section 3, the particle transport and distribution in the curved slot are more complicated than that of the straight slot. It is meaningful to discuss the crucial findings of this investigation in detail.
Conclusion
In this investigation, experimental methods were conducted to study the particle transport in narrow, curved slots. The sensitivity analysis was performed to study the particle distribution in a curved slot by changing the bending angle, fluid velocity, particle size, particle density, and particle volume fraction. However, there are still three limitations. First, the slot walls are smooth acrylic, while the fracture surface is very rough, significantly disturbing the particle behavior.
Credit author statement
Hai Qu: Conceptualization, Methodology, Validation, Funding acquisition; Yushuang Hu: Investigation, Formal Analysis, Visualization; Ying Liu: Writing-Original draft preparation, Supervision, Project administration. Hun Lin: Revising and Error analysis. Rui Wang: Formal Analysis, Data Curation, Visualization. Shimao Tang: The design of experimental slots. Ling Xue: The experimental conduction.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was supported by Chongqing Research Program of Basic Research and Frontier Technology(Grant No. Cstc2019jcyj-msxmX0006), Science and Technology Research Program of Chongqing Municipal Education Commission of China(Grant No. KJQN201801530, KJQN201901511).
References (50)
- et al.
Effects of angle patterns at fracture intersections on fluid flow nonlinearity and outlet flow rate distribution at high Reynolds numbers
Int. J. Rock Mech. Min. Sci.
(2019) - et al.
Proppant transport in a scaled vertical planar fracture: vorticity and dune placement
J. Petrol. Sci. Eng.
(2019) - et al.
Three-dimensional lattice simulation of hydraulic fracture interaction with natural fractures
Comput. Geotech.
(2019) - et al.
Dynamic bridging of proppant particles in a hydraulic fracture
Int. J. Eng. Sci.
(2019) - et al.
Incipient motion behavior of the settled particles in supercritical CO2
J. Nat. Gas Sci. Eng.
(2019) - et al.
Effect of proppant addition schedule on the proppant distribution in a straight fracture for slickwater treatment
J. Petrol. Sci. Eng.
(2018) - et al.
Numerical simulation on solid-liquid two-phase flow in cross fractures
Chem. Eng. Sci.
(2018) - et al.
Particle transport in laboratory models of bifurcating fractures
J. Nat. Gas Sci. Eng.
(2016) Fluid mechanics of hydraulic fracturing: a review
J. Petrol. Sci. Eng.
(2017)- et al.
Power law correlations for sediment transport in pressure driven channel flows
Int. J. Multiphas. Flow
(2002)
Quantitative and visual analysis of proppant transport in rough fractures
J. Nat. Gas Sci. Eng.
Proppant transport in complex fracture networks – a review
J. Petrol. Sci. Eng.
Calculation of proppant-carrying flow in supercritical carbon dioxide fracturing fluid
J. Petrol. Sci. Eng.
Proppant transport study in fractures with intersections
Fuel
A visualization study of proppant transport in foam fracturing fluids
J. Nat. Gas Sci. Eng.
Bi-power law correlations for sediment transport in pressure driven channel flows
Int. J. Multiphas. Flow
Numerical simulations of proppant deposition and transport characteristics in hydraulic fractures and fracture networks
J. Petrol. Sci. Eng.
CFD study of sand erosion in pipeline
J. Petrol. Sci. Eng.
Experimental investigation of proppant settling in complex hydraulic-natural fracture system in shale reservoirs
J. Nat. Gas Sci. Eng.
Numerical simulation of proppant transport in hydraulic fracture with the upscaling CFD-DEM method
J. Nat. Gas Sci. Eng.
Numerical simulation of proppant transport in propagating fractures with the multi-phase particle-in-cell method, Fuel
Numerical simulation of proppant distribution in hydraulic fractures in horizontal wells
J. Nat. Gas Sci. Eng.
Hydrodynamic and mechanical behavior of multi-particle confined between two parallel plates
Adv. Powder Technol.
CFD-DEM simulation of proppant transport by supercritical CO2 in a vertical planar fracture
J. Nat. Gas Sci. Eng.
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2022, Petroleum ScienceCitation Excerpt :The slurry flows out of the slots discharged through the five holes on the outlet panel to the recycle tank. The inlet and outlet configurations are similar to the channel in the literature (Ba Geri et al., 2018; Fernández et al., 2019; Mack et al., 2014; Qu et al., 2021a). The channel is assembled by two transparent acrylic panels and achieves the sizes of 1.5 m (length) × 0.27 m (height) × 3 mm (width).
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2022, International Journal of Multiphase FlowCitation Excerpt :Correspondingly, the narrow complicated pathways change the flow pattern and proppant distribution due to the violent interactions of the particle to wall and particle to particle (Lin et al., 2020; Qu et al., 2021c; Zhang et al., 2019). Since proppant transport and placement directly govern productivity, understanding the proppant-fluid flow in a complex pathway has received considerable critical attention (Qu et al., 2021a; Sahai and Moghanloo, 2019). Particle transport within a single planar fracture, which is the same as the scenario of crossing in Fig. 1(a), has been widely investigated by a variety of straight slots (Babcock et al., 1967; Barree and Conway, 1994; Kern et al., 1959; Wang et al., 2003).